Speaker: Yichen Ma, Cornell University
Title: Enumeration of flags in partial orders and convex geometries
Time: 2:30 PM, Monday, March 11, 2024
Place: Malott 206
Abstract: We consider a Hopf monoid of partial orders and another of
convex geometries, and investigate combinatorial invariants
constructed from characters on them. Each invariant comes in a pair
consisting of a polynomial and a (more general) quasisymmetric
function.
For partial orders we obtain the order polynomial of Stanley and the
enriched order polynomial of Stembridge. For convex geometries we
obtain polynomials first introduced by Edelman-Jamison and
Billera-Hsiao-Provan. We obtain reciprocity results satisfied by these
polynomials from the perspective of characters in a unified manner.
We describe the coefficients of the quasisymmetric invariants as
enumerating faces on certain simplicial complexes. These include the
barycentric subdivision of the CW-sphere of a convex geometry.
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